Colloidal Drop Spreading, Evaporation and Particle Deposition – A Lattice Boltzmann StudyAbhijit S. Joshi and Ying Sun, Complex Fluids and Multiphase Transport Lab

Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia PA 19104

Evaporation with a “Pinned” Contact Line

For rough surfaces, experiments reveal that the contact line can remain pinnedduring drop evaporation until the receding contact angle is reached. The LBMsimulation above demonstrates this effect for a receding contact angle of 15°. Likeexperiments, suspended particles inside the liquid are observed to flow towardsthe contact line in the LBM.

Isothermal Evaporation Model

Effect of Drop Spacing on Deposit Morphology

A large spacing between successive drops (top row) leads to isolated deposits.When the spacing between the drops is reduced (bottom row), the spreadingcontact lines of adjacent drops connect with each other and the final depositshows continuity. Reducing spacing between drops can lead to line deposits.

Inkjet printer nozzle

FlexibleSubstrate

Liquid drop with suspended material

Functional material deposit

z

yx

Motivation: Functional Material Deposition using Inkjet Printing

0.70 1.04 1.40

Drop spacing / Drop diameter

Initi

al p

artic

le v

olum

e fr

actio

n

Morphology Map: Final Particle Deposition

10%

5%

Conclusions & Future WorkVapor outflow boundary

condition induces isothermal evaporation of the liquid drop

Fixed solid substrate

Suspended solid particles

Vapor

Liquid

Lattice Boltzmann Method

SUBSTRATE

1

3

2

LIQUIDVAPOR

A three-dimensional (3D), multi-phase (liquid + vapor) particle suspension model has been developed based on the 2D model of Joshi and Sun (2009)*. The computer code has been developed using FORTRAN 90 and runs on a parallel supercomputer.

Suspended particles are spherical in shape and their motion is coupled to the fluid flow.

Inter-particle forces prevent particles from overlapping with each other, or with the solid substrate at the bottom.

Particles can be trapped by the liquid-vapor interface.

* Joshi A. S. and Sun Y. (2009) Physical Review E, 79, 066703

Self-Similar Evaporation (Moving Contact Line)

Acknowledgments: Support for this work was provided by the National ScienceFoundation (Grant No. CAREER-0846825) and the American Chemical SocietyPetroleum Research Fund (Grant No. 47731-G9).

The lattice Boltzmann method (LBM) is a useful computational tool to investigatethe fundamental physical processes during deposition of functional materialsusing inkjet printing.

Experimentally observed processes like contact line pinning can be modeled withease.

The final particle deposits can be studied as a function of process parameters inorder to optimize the process and obtain repeatable results.

Future work will consist of experimental validation of the model and extension tosimulate deposition of non-spherical (ellipsoidal) particles.

x

z

Peri

odic

bou

ndar

y

Peri

odic

bou

ndar

y

z

yx

z

y x

This type of evaporation is observed for smooth substrates with no physical orchemical heterogeneities. Most of our results so far have been obtained for suchan “ideal” substrate. The contact angle remains unchanged throughout theevaporation process.

Lx

L Y

D

Number of suspended particles

Suspended particle radius

Initial liquid drop diameter

Initial spacing between adjacent (periodic) liquid drops

Evaporation rate (suction velocity at the top of the domain)

Equilibrium contact angle

L Y

D

RP

NP

U Z

θeq

LBM Parameters for Obtaining Line Deposits

x

y

87 particles / drop

44 particles / drop

Contact line